Respuesta :
Answer:
The probability that a pipe produced has length greater than 30 feet is 0.5385.
Step-by-step explanation:
Let X = product lengths of the pipes produced by a company.
The random variable X is Uniformly distributed with parameters a = 28.50 feet to b = 31.75 feet.
The probability density function of Uniform random variable is:
[tex]f_{X}(x)=\left \{ {{\frac{1}{b-a};\ a<X<b,\ a<b} \atop {0;\ otherwise}} \right.[/tex]
Compute the probability that a pipe produced has length greater than 30 feet as follows:
[tex]P (X>30)=\int\limits^{31.75}_{30} {\frac{1}{31.75-28.50}} \, dx \\[/tex]
[tex]=\frac{1}{3.25}\times \int\limits^{31.75}_{30} {1} \, dx \\[/tex]
[tex]=\frac{1}{3.25}\times [31.75-30][/tex]
[tex]=0.538462\\\approx0.5385[/tex]
Thus, the probability that a pipe produced has length greater than 30 feet is 0.5385.
